I have recently thought about building ESL speakers. I have looked all over and understand how to build the panels and where to get everything. I just cant figure out how to find the right stuff to build the transformer part of it. I have found many transformers but I can't figure out how to know if its the right kind. I was interested on using the Toroid transformers as they were more inexpensive. I am pretty sure I understand how to wire them but not positive. Could anyone help me understand how to choose the right transformers. I was planing on building panels that were about 6-4 feet tall by 1-2 feet wide. I would like them to go down to about 100-200 Hz.

Also I was planning on running these speakers off of a Harmon Kardon home theater receiver. Is this even possible or do I need to find another amplifier. Thanks.

If you never tried winding your own trannys it probably wont be worth your time. If you care about clean sound insuring a good one, then leave it to the pros. There are a lot of good ones out their, I only found one company that actual shows you how the transformer responds under a capacator load, must of the response graphs of other companies transformers were tested under resistance loads. This is sort of useless to us ESL builders, since ESLs are capacitor loads to amps. The company I found is called PLITRON. They are expensive. You said toriods are cheaper, i think you have it backwards, they are the ones to use but arent cheap. You can look them up on a search it will come up. Im waiting to get mine, they have two week lead time.

I think you should probably rethink the design. Im pretty sure that HK reciever is a no go, especially if you want the cell to produce bass. To get bass you need a lot of power. ESL's have poor low freq. response due to phase cancellation (assuming your making a dipole radiator), when the back wave reflects off the wall and interfere with the outgoing front waves, the low freq back waves when they make it to the front will be out of phase with them causeing a severve drop in your output SPL. A rule of thumb states that phase cancellations will creep in at a wavelengh = 1/4* shortest cell dimension. A baffle would help prevent this, an equalizer would help too.

I started to build a pair of perf. stators, wires are probably better, hard to do. I will Xover somewhere near 400-500Hz to a traditional woofer. Some kind of TL design. My panels are roughly 12"x40" curved. Someone wiser than me gave good advise, dont try to make a full-range as a first build. Choose something simplier and work up to it. Besides I dont know what success people have with full-range ESls. A hybrid design is more practical.

your problem is understandeable, because in most texts about ESLs most of what is written about the trannies is useless or rubbish.
The usual "Just wire a 5k/8Ohms Tubeamp-tranny backwards" doesn´t help much though it adresses the main point of design interest: impedance matching.

So to choose the right tranny you need to know the capacity of your panel, which requires the d/s and the panel´s area.

If you´ve found the transformation factor you have to decide wether to use a lowloss tranny or a higher loss tranny. With a lowloss part (like a toroid) the complex impedance of the ´capacitor´ is transformed with a high degree of phaseshift (>80° possible) to the primary side. Its a difficult task for the amp to drive such a complex load and most amps fail.
With the higher loss part (EI-cores with low section count), the phaseshift might stay below 45° which lowers the drive problem considerably. On the other hand this part will show a reduced bandwidth.

So the choice depends on several factors that you can trade against each other. You have to be sure about those parameters before you can choose the right tranny.

You answered a lot of my questions. So basically what I would need to do is build the panels first and find out the capacity of the panel and then match the transformer to that. I will also probably have to run them off their own amp as the receiver would not be able to handle them. To make it a little easier I could do a hybrid design so I don't have to go so low on the panels.

So once I find the capacity of the panels how do I choose how big of a transformer I need?

Also what would be a good amp preferably used that would be able to run a pair of the panels?

I always recommend to let the ESL do what it can do best and better than any dynamic speaker----and that is to reproduce the freq-range above >100Hz. Powerwise this is a relativ moderate demand (and would be so even if it had to reproduce bass) if the amp can handle the phase shift, i.e. the reactive power demand.

So lets say you´d cross the panel over at >200Hz. Then You could use high mechanical tension on the membrane giving a fs of 100-150Hz.
You´d need 1mm of d/s or slightly more. This will give enough SPLmax with a larger panel of the area you mentioned before. Using sheet metal without segmentation You end up at lets say ~2nF capacitance which translates to ~4kOhms@20kHz. If the impedance should not drop much below 1Ohms on the primary side you need a transformation factor of sqr(4000) --> 63. To reach a bandwidth of just above 20kHz you´d need a lowloss tranny like the Plitron. The Plitron (Amplimo) come in 50:1 and 75:1. Alternatively a pair of 230V/7V power toroids connected in series/parallel give ~60:1 (estimated ~90% efficiency).
Both the Plitron and the pair of toroids will yield phaseshifts of >80° around 4-6kHz! This asks for a very stable amp since for every real watt between 5 to 10 reactive watts are wasted! Aside huge Class A or AB amps (preferably without global feedback) class-d amps handle such loads quite well and are cheaper.